Finite Dimensional Vector Spaces Are Complete for Traced Symmetric Monoidal Categories

Masahito Hasegawa; Martin Hofmann; Gordon D. Plotkin

doi:10.1007/978-3-540-78127-1_20

Finite Dimensional Vector Spaces Are Complete for Traced Symmetric Monoidal Categories

Masahito Hasegawa, Martin Hofmann, Gordon D. Plotkin

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We show that the category FinVect k of finite dimensional vector spaces and linear maps over any field k is (collectively) complete for the traced symmetric monoidal category freely generated from a signature, provided that the field has characteristic 0; this means that for any two different arrows in the free traced category there always exists a strong traced functor into FinVect k which distinguishes them. Therefore two arrows in the free traced category are the same if and only if they agree for all interpretations in FinVect k .

Original language	English
Title of host publication	Pillars of Computer Science
Subtitle of host publication	Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday
Publisher	Springer Berlin Heidelberg
Pages	367-385
Number of pages	19
Volume	4800
ISBN (Electronic)	978-3-540-78127-1
ISBN (Print)	978-3-540-78126-4
DOIs	https://doi.org/10.1007/978-3-540-78127-1_20
Publication status	Published - 2008

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10.1007/978-3-540-78127-1_20

Hasegawa Hormann ET AL 2008 Finite Dimensional Vector Spaces are Complete for Traced Symmetric Monoidal CategoriesAccepted author manuscript, 285 KB

http://dx.doi.org/10.1007/978-3-540-78127-1_20

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Finite Dimensional Vector Spaces Are Complete for Traced Symmetric Monoidal Categories. / Hasegawa, Masahito; Hofmann, Martin; Plotkin, Gordon D.

Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday. Vol. 4800 Springer Berlin Heidelberg, 2008. p. 367-385.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AB - We show that the category FinVect k of finite dimensional vector spaces and linear maps over any field k is (collectively) complete for the traced symmetric monoidal category freely generated from a signature, provided that the field has characteristic 0; this means that for any two different arrows in the free traced category there always exists a strong traced functor into FinVect k which distinguishes them. Therefore two arrows in the free traced category are the same if and only if they agree for all interpretations in FinVect k .

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BT - Pillars of Computer Science

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Finite Dimensional Vector Spaces Are Complete for Traced Symmetric Monoidal Categories

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